As a proof of concept, we implement such a scan in what is arguably the simplest non-trivial case: namely rank-two theories whose Schur indices satisfy a fourth-order untwisted MDE. As will be reviewed below, such MDEs—as well as their solutions—are specified by three terms in the Fourier expansion of \(\chi _0(q)\) . We must then scan over these three parameters, and for each triplet apply our algorithm to check if the proposed vacuum character admits a 4d interpretation. Remarkably, of the order \(O(10^{11})\)  candidate triplets that we examine, only 15 pass the full set of moduli space and unitarity constraints imposed in our algorithm. The data of these 15 cases is summarized in Table REF  and Figure REF . An even more careful analysis (using tools which are difficult to automate on a computer) allows us to rule out nine of the 15 theories,More precisely, seven candidates will be rigorously ruled out, while two will be shown to be implausible. leaving only six candidates. Comparing to the lists in e.g. [1]}, all six candidates can be seen to correspond to known physical \({\cal N}=2\)  theory.
